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1. Which of the differential equations is/are non linear?

a. Only I

b. Only II

c. Only I and III

d. Only II and IV

e. None of the above

2. Which is a solution to the following DE? yy'-ye

^{t}=t

^{2}e

^{2t}

a. y=t

^{2}(e

^{t})

b. y= (t-1)e

^{t}(Incorrect answer)

c. y= te

^{t}

d. y= (t+1)e

^{t}

e. None of the above

3. For the linear DE xy'=x

^{4}e

^{x}+2y which of the following is an integrating factor 𝜇(x)?

a. x

^{3}

b. x

^{-3}

c. e

^{x}

d. xe

^{x}

e. None of the above (My professor says this is NOT the correct answer).

4. Given that y1= x is a solutio to x

^{2}y''+xy'-y=0, x>0, Find the other fundamental solution.

a. y2=x

^{-2}

b. y2=x

^{-1}

c. y2=x

d. y2= x

^{2}(Incorrect answer)

e. None of the above